解题方法
1 . 在平面直角坐标系中,矩形OABC的边OC、OA分别在x轴、y轴上,点A(0,m),点C(n,0),且m、n满足
+
=0.
(1)求点A、C的坐标;
(2)如图1,点D为第一象限内一动点,连CD、BD、OD,∠ODB=90°,试探究线段CD、OD、BD之间的数量关系,并证明你的结论;
(3)如图2,点F在线段OA上,连BF,作OM⊥BF于M,AN⊥BF于N,当F在线段OA上运动时(不与O、A重合),
的值是否变化?若变化,求出变化的范围;若不变,求出其值.
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2e63c6d29688509feea8149cd86c45a5.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/c5127cfcfbaf2129afb95649ab8ccfc1.png)
(1)求点A、C的坐标;
(2)如图1,点D为第一象限内一动点,连CD、BD、OD,∠ODB=90°,试探究线段CD、OD、BD之间的数量关系,并证明你的结论;
(3)如图2,点F在线段OA上,连BF,作OM⊥BF于M,AN⊥BF于N,当F在线段OA上运动时(不与O、A重合),
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03ca0f4ff1cd41df9357267608e405ee.png)
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2021-04-07更新
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3卷引用:2021年浙江省温州市苍南县中考数学第一次摸底试题
2021年浙江省温州市苍南县中考数学第一次摸底试题(已下线)数学-(绍兴卷)-【试题猜想】2021年中考考前最后一卷重庆市忠县花桥镇初级中学、马灌初级中学校2023-2024学年八年级下学期期中考试数学试题
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2 . 如图,在
中,
,以
为直径的
与
交于点
,连接
.
(1)尺规作图:作出劣弧
的中点
(不写作法,保留作图痕迹)
(2)连接
交
于
点,连接
,求证:
;
(3)若
的半径等于12,且
与
相切于
点,求阴影部分的面积(结果保留
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/6/15/ebb4398b-75bb-4613-a822-d7e3704d0ae8.png?resizew=185)
(1)尺规作图:作出劣弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f9353ca110c8b81561455b232dbc15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc638733d0c4e20814cb311074e446a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/ff4489d9b83072184c0e1d6b09be50ca.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/86ebba6ed1add0fe647c0226614b9290.png)
您最近一年使用:0次
3 . 如图,在
中,
,以
为直径的
与
交于点
,连接
.
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/6/4dfd2420-e7d6-4dc5-88c4-c4851d5fadea.png?resizew=229)
(1)尺规作图:作出劣弧
的中点
(不写作法,保留作图痕迹);
(2)连接
交
于
点,连接
,求证:
;
(3)若
的半径等于6,且
与
相切于
点,求阴影部分的面积(结果保留
).
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/047dc9795efa99b6fb9fdf9778085dab.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f52a58fbaf4fea03567e88a9f0f6e37e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0dc5c9827dfd0be5a9c85962d6ccbfb1.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/8455657dde27aabe6adb7b188e031c11.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://img.xkw.com/dksih/QBM/editorImg/2023/5/6/4dfd2420-e7d6-4dc5-88c4-c4851d5fadea.png?resizew=229)
(1)尺规作图:作出劣弧
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/f6f9353ca110c8b81561455b232dbc15.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/2a30f3a8b673cc28bd90c50cf1a35281.png)
(2)连接
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/85c4bdfb0db1e31e8459df1d15f9ab55.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/03902478df1a55bc99703210bccab910.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a0ed1ec316bc54c37c4286c208f55667.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/68a83fdd2ba72a2dba0b6b10bb3e06b9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3dc638733d0c4e20814cb311074e446a.png)
(3)若
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3d97cdc586744d208b6f69c9813af977.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/60ef95894ceebaf236170e8832dcf7e3.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/5963abe8f421bd99a2aaa94831a951e9.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/70f5389990c3a0c5373f3bd9fb2454c9.png)
您最近一年使用:0次
真题
4 . 问题探究:
小红遇到这样一个问题:如图1,
中,
,
,AD是中线,求AD的取值范围.她的做法是:延长AD到E,使
,连接BE,证明
,经过推理和计算使问题得到解决.
请回答:(1)小红证明
的判定定理是:__________________________________________;
(2)AD的取值范围是________________________;
方法运用:
(3)如图2,AD是
的中线,在AD上取一点F,连结BF并延长交AC于点E,使
,求证:
.
(4)如图3,在矩形ABCD中,
,在BD上取一点F,以BF为斜边作
,且
,点G是DF的中点,连接EG,CG,求证:
.
小红遇到这样一个问题:如图1,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/305a88d4e0249bd16d48eda01331d2d4.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/a8a7b5adfcac0f46a4cd19da4ebb4a2b.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/0ad98ad714864041a632ca949308e417.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/440095115d64b74e4b1c30e402c178e1.png)
请回答:(1)小红证明
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/440095115d64b74e4b1c30e402c178e1.png)
(2)AD的取值范围是________________________;
方法运用:
(3)如图2,AD是
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/15c0dbe3c080c4c4636c64803e5c1f76.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3767efa8adfb71001ad39df9560cbf6a.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/fe8bb808edb7f81fb3c14c8f3d7f0fad.png)
(4)如图3,在矩形ABCD中,
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/3a54049b5c43495c4f00f7a364cc5b8e.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/d81b4e95f60e84d23e650fc70be62874.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/72b9bf93660eb49c1b049595f5f7700d.png)
![](https://staticzujuan.xkw.com/quesimg/Upload/formula/953b741d481bb5d5536688d6d4c22962.png)
![](https://img.xkw.com/dksih/QBM/2020/7/16/2507220733640704/2507240025325568/STEM/e0d68739-95e9-4afb-b2a4-a602485c557a.png)
您最近一年使用:0次
2020-07-16更新
|
5881次组卷
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7卷引用:山东省德州市2020年数学中考试题
山东省德州市2020年数学中考试题湖北省襄阳市宜城市2020-2021学年九年级上学期期末数学试题(已下线)(专题)全等三角形的常见辅助线2020-2021学年青岛版九年级数学上册第一单元 图形的相似提升卷2021年山东省枣庄市台儿庄区中考数学模拟试卷(二)(已下线)黄金卷02(青岛专用)-【赢在中考·黄金8卷】备战2023年中考数学全真模拟卷2024年内蒙古包头市九年级中考预测卷数学模拟预测题